Jean-Francois Bariant

Tracking objects with multiple reflections based on ultrasonic transducer raw data using a PDAF

When mounted on a vehicle bumper, ultrasonic transducer signal contains information from valid objects as well as ground reflections. In order to remove ground echoes, the classic approach is to use thresholds to filter reflections of small amplitude. However, valid object reflections can frequently occur beneath the ground thresholds, reducing the detection rate of the sensor. We present an approach where tracks are initialized only with echoes above the ground thresholds, but updated with all echoes using a PDAF. As objects can often reflect a second echo, we propose a modification of the PDAF to avoid interference between the first echo real object position and the second echo. Simulation and real measurements both show the advantage of our method which improves tremendously the detection rate.

A numerically stable formulation of the square root unscented Kalman filter for state estimation

The square root unscented Kalman filter was introduced to provide a more numerically robust formulation of the unscented Kalman filter and to guarantee positive semi-definiteness. The filter maintains the Cholesky factor of the covariance matrix instead of the covariance itself. Efficient linear algebra techniques, including Cholesky update and downdate, are used to predict and update the Cholesky factor over time. However, a downdated Cholesky factor may not exist due to numerical rounding and truncation. This may impose issues especially in highly dimensional state spaces or if quantities of different magnitude are involved. A failed Cholesky downdate could be accounted for by predicting a more conservative covariance matrix or by neglecting the filter step in the prevailing iteration. However, both approaches may decrease filter performance. A more sophisticated strategy would be to prevent these issues from happening in the first place. We propose a mathematically equivalent filter that numerically guarantees positive semi-definiteness for any arithmetic precision at the cost of a negligible runtime increase. It applies the auxiliary formulation of the scaled unscented transform and filters the forecast sigma points separately.